本题目来源于试卷: Complex Numbers，类别为 IB数学
[问答题]
Consider the complex numbers a(1pwvb:*haa xc4a;p qu.fg4 :17ke4v ftf *:appgqqdogysn )gx 6+2$z_{1}=3 \operatorname{cis}\left(120^{\circ}\right)$ and $z_{2}=2+2 \mathrm{i}$ .
1. Calculate $\frac{z_{1}}{z_{2}}$ giving your answer both in modulus-argument form and Cartesian form.
2. Use your results from part (a) to find the exact value of $\sin 15^{\circ} \cdot \sin 45^{\circ} \cdot \sin 75^{\circ}$ , giving your answer in the form $\frac{\sqrt{a}}{b} where a, b \in \mathbb{Z}^{+}$ .
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